Performance Evaluation and Parametric Optimum Criteria of an Irreversible Molten Carbonate Fuel Cell-Heat Engine Hybrid System

Transcription

1 Int. J. Elctrochm. Sci., 6 () Intrnational Journal of ELECTROCHEMICAL SCIENCE Prformanc Evaluation Paramtric Optimum Critria of an Irrvrsibl Moltn Carbonat Ful Cll-Hat Engin Hybrid Systm Houchng Zhang, Guoxing Lin, Jincan Chn Dpartmnt of Physics, Xiamn Univrsity, Xiamn 365, Popl s Rpublic of China gxlin@xmu.du.cn, jcchn@xmu.du.cn Rcivd: August / Accptd: Sptmbr / Publishd: Octobr Th modl of a hybrid systm composd of a moltn carbonat ful cll (MCFC) a hat ngin is prsntd, in which multi-irrvrsibilitis such as ovrpotntials in th lctrochmical raction, hat lak from th MCFC to th nvironmnt, non-prfct rgnration in th rgnrator, finit-rat hat transfr in th hat ngin ar takn into account. Exprssions for th fficincy powr output of th systm ar analytically drivd, from which th gnral charactristics of th hybrid systm ar rvald th optimum critria of som main paramtrs such as th currnt dnsity, fficincy powr output ar dtrmind. Th influnc of th irrvrsibl losss on th prformanc of th hybrid systm is discussd. Morovr, a multi-objctiv function including both th fficincy th powr output is put forward usd to furthr subdivid th optimally oprating rgion of th hybrid systm. Th rsults obtaind hr ar vry gnral may b dirctly usd to driv th various intrsting conclusions of th hybrid systms opratd undr diffrnt spcial cass. Kywords: Moltn carbonat ful cll; Hat ngin; Hybrid systm; Irrvrsibility; Optimum analysis. INTRODUCTION Th dual ffcts of th limitd fossil ful sourcs nvironmnt pollution hav shown th rquirmnt of innovativ nrgy gnration systms to not only incras fficincy but also rduc harmful missions. Th ful cll is an lctrochmical nrgy convrsion systm which dirctly convrts chmical nrgy in a ful to lctricity. This rsults in high fficincy low pollutant missions in comparison with traditional fossil-basd nrgy convrsion dvics [-6]. Among th various ful clls, th moltn carbonat ful cll (MCFC) is vry promising bcaus of its ful flxibility high oprating tmpratur [7-]. Th high tmpratur oprating charactristics

2 Int. J. Elctrochm. Sci., Vol. 6, 475 provid th possibility of cognration with othr typs of powr gnrators such as gas turbins [- 4] or hat ngins [5-8], so that th prformanc of th MCFC hybrid systms can b nhancd. Sinc th concpt of ful cll-hat ngin hybrid systms was proposd, a numbr of thortical xprimntal invstigations hav bn carrid out, which includ th thrmodynamic analysis [5-7], th finding promising bottoming cycls [8, 9], th plant configurations [, ], so on [, 3]. Howvr, what is th uppr bound of prformanc for th MCFC hybrid systm? It is still an intrsting problm that has not solvd yt. It is wll known that for th various hat ngins opratd at btwn two hat rsrvoirs, th fficincy obtaind by th Carnot hat ngin is imum. Thus, it will b an availabl mthod to thortically dtrmin th imum fficincy powr output of th MCFC-hat ngin hybrid systm if th Carnot hat ngin is connctd with th MCFC. In th prsnt papr, th prformanc th paramtric chosn critria of th MCFC-hat ngin hybrid systm will b analyzd discussd systmatically. Th concrt contnts ar arrangd as follows. In Sc., th modl of th MCFC-hat ngin hybrid systm consisting of an MCFC, a rgnrator a hat ngin is stablishd ach assmbly unit in th hybrid systm will b mathmatically dscribd. Th fficincy th powr output of th hybrid systm ar analytically drivd. In Sc. 3, th gnral prformanc charactristics of th hybrid systm ar rvald th optimum critria of som main prformanc paramtrs ar dtrmind. A multi-objctiv function is usd to furthr xpound how to giv considration to both th fficincy th powr output of th hybrid systm. In Sc. 4, th ffcts of som synthsizd paramtrs rprsnting th irrvrsibl losss on th prformanc of th hybrid systm ar discussd in dtails. Som significant rsults for svral spcial cass ar dirctly obtaind. Finally, som important conclusions ar summarizd.. DEPICTION OF AN IRREVERSIBLE MCFC-HEAT ENGINE HYBRID SYSTEM Figur shows th schmatic diagram of an MCFC-hat ngin hybrid systm composd of an MCFC, a hat ngin, a rgnrator, whr T is th nvironmnt tmpratur, T is th working tmpratur of th MCFC, P M P H ar th powr outputs of th MCFC hat ngin, q h is th rat of hat transfr btwn th MCFC th hat ngin, q l is th rat of hat transfr btwn th hat ngin th nvironmnt, q Loss is th rat of hat losss from th MCFC to th nvironmnt. In Fig., th MCFC acts as th high-tmpratur hat rsrvoir of th hat ngin for a furthr powr production th rgnrator in th hybrid systm is to prhat th incoming ractants by mans of th hat in th high tmpratur products. By using such a hybrid systm, th hat producd in th MCFC can b fficintly utilizd, consquntly, th prformanc of th MCFC systm can b improvd. Blow, vry assmbly unit in th hybrid systm will b, rspctivly, discussd in th nxt svral subsctions.

3 Int. J. Elctrochm. Sci., Vol. 6, 476 Figur. Th schmatic diagram of an MCFC-hat ngin hybrid systm.. An irrvrsibl MCFC Figur. Th schmatic diagram of an MCFC.

4 Int. J. Elctrochm. Sci., Vol. 6, 477 Many rsarchrs hav laboratly dmonstratd th oprating mchanism of th MCFC [7, 9, 4-7]. Hr, w only giv a simpl dscription for an MCFC. As shown in Fig., an MCFC is opratd by introducing hydrogn to th anod oxygn carbon dioxid (if ncssary) to th cathod, rspctivly. At th anod hydrogn racts with carbonat ions availabl in th carbonat lctrolyt into watr carbon dioxid rlass lctrons to th xtrnal lctric circuit, i.., H CO3 HO CO. At th cathod oxygn racts with carbon dioxid lctrons into carbonat ions, i.., O CO CO3. Th ovrall lctrochmical raction is H O, CO, cat HO CO an lctricity hat, () whr subscripts an cat indicat anod cathod, rspctivly. To sustain th total lctrochmical raction, th producd carbon dioxid is transportd from th anod to th cathod whil th producd carbonat ions flow from th cathod to th anod. It should b pointd out that th ovrall raction is xo-nrgtic. Ths nrgis includ an lctric part, which is consumd in th xtrnal lctric circuit, a thrmal part, which can b usd for furthr powr production by th hat ngin, i.., H G TS, whr H is th total nrgy rlasd by th raction, G is th lctric part TS is th thrmal part. According to Faraday s law, hydrogn consumption rat in th lctrochmical raction is dtrmind by q = I /( n F) H, whr I is th oprating lctric currnt, n is th numbr of lctrons, F is Faraday s constant [8, 9]. Thus, th imum possibl nrgy (both lctrical thrmal) rlasd by th ractions is [5] H q H h Ih n F, () whr 3]. h is th stard molar nthalpy chang can b calculatd from th data in Rfs. [8, 3- It is wll known that th masurd opn circuit voltag U cll in a practical ful cll is always U dtrmind by Nrnst quation [5, 33-35] bcaus thr lowr than th idal rvrsibl voltag xist som irrvrsibl losss rsulting from th anod ovrpotntial ohmic ovrpotntial 36]: U U an, cathod ovrpotntial U cat, U. Th thr ovrpotntials can b, rspctivly, xprssd as [4, 6, 34, ohm E RT 9 act, an.4.7. an.7 j xp ph,an pco,an pho,an, (3) U 7.55 E j xp RT p act, cat.43.9 cat O,cat CO,cat, (4) p

5 Int. J. Elctrochm. Sci., Vol. 6, U ohm.5 j xp 36, (5) T 93 whr j is th oprating currnt dnsity; R is th univrsal gas constant; E act is th activation nrgy, p ar th partial prssurs of spcis k at th anod or cathod. It should b pointd out that th k anod ovrpotntial can b achivd its minimum whn th anod gas inlt compositions ar optimally chosn. By using numrical calculation, th concrt valus of th optimal anod gas compositions undr th diffrnt H concntrations ar listd in Tabl. Furthrmor, th cathod ovrpotntial dcrass whn th O /or CO concntrations ar incrasd. Tabl. Th optimal anod gas compositions undr th diffrnt H concntrations. H concntration (%) CO concntration (%) H O concntration (%) With th hlp of th abov analysis, th fficincy powr output of an irrvrsibl MCFC may b, rspctivly, xprssd as M PM H nf ( U Uan Ucat Uohm ) h (6) P U I ( U U U U ) I, (7) M cll an cat ohm whr MCFC. I ja is th lctric currnt through th MCFC A is th ffctiv surfac ara of th. An irrvrsibl rgnrator Th rgnrator in th hybrid systm actd as a hat xchangr, hating th inlt ractants from th ambint tmpratur to th tmpratur of MCFC by using th high-tmpratur products. Whn th rgnrativ fficincy of th rgnrator is qual to, th rgnrativ procss is idal th additional hat is unncssary. It should b pointd out that owing to th xistnc of th thrmal rsistanc, th rgnrativ losss ar invitabl. It is rasonabl to assum that th rat of th

6 Int. J. Elctrochm. Sci., Vol. 6, 479 rgnrativ losss is dirctly proportional to th tmpratur diffrnc btwn th MCFC th nvironmnt [37, 38], i.., q U A ( )( T T ), (8) r r r whr U r A r ar, rspctivly, th hat-transfr cofficint hat-transfr ara btwn th rgnrator th nvironmnt. In ordr to rplnish th hat losss in th rgnrativ procss, th additional hat may b usually transfrrd from th MCFC at tmpratur T to th inlt ractants in th rgnrator in tim so that th xport tmpratur of th inlt ractants is nsurd to attain th working tmpratur of th MCFC..3 An ndorvrsibl hat ngin For th hat ngin in th hybrid systm, th MCFC working at tmpratur T can b takn as to b a high tmpratur hat rsrvoir th nvironmnt is a low tmpratur rsrvoir. Thus, w can us a Carnot hat ngin to furthr convrt th hat producd in th MCFC into powr. For th sak of simplification, th cyclic modl of th hat ngin is assumd to b ndorvrsibl [5, 39] hat transfr btwn th hat ngin th hat rsrvoirs obys Nwton s law [5, 4]. It has bn provd that for givn rat of hat input q total hat-transfr ara A of th hat ngin, whn th h condition A / A U / U is satisfid, th fficincy of th hat ngin may b xprssd as [5, 4, 4] h T / ( T q / K), (9) H h whr = U U A /( U U ) K h is a paramtr to masur th irrvrsibility of finit-rat hat + transfr in th hat ngin, Ah A A, A A ar th hat-transfr aras btwn th hat ngin th two hat rsrvoirs, U U ar th hat-transfr cofficints btwn th hat ngin th two hat rsrvoirs. According to Fig., on can driv th rat of hat input from th MCFC to th hat ngin as q H P q q, () h M r Loss whr th hat loss q Loss from th MCFC to th nvironmnt may b xprssd as [4, 4, 43] q U A ( T T ), () Loss 3 3 U 3 is th convctiv /or conductiv hat-lak cofficint, A 3 is th ffctiv hattransfr ara.

7 Int. J. Elctrochm. Sci., Vol. 6, 47 By using Eqs. (8)-(), th fficincy powr output of th hat ngin may b, rspctivly, xprssd as H T / T m [( ) j m ( T / T )] M () Ah PH qhh [( M ) j m( T / T)]{ }, (3) n F T / T m [( ) j m ( T / T )] M whr Ah U3A3U r Ar ( ) m m. n FKT A h / ( n FT ).4 Th fficincy powr output of th hybrid systm Tabl. Paramtrs usd in th modling of th MCFC-hat ngin hybrid systm [4, 34, 36]. Paramtr Valu Faraday constant, F (C mol - ) 96,485 Numbr of lctrons, n Univrsal gas constant, R (J mol - K - ) 8.34 Oprating tmpratur, T (K) 893 Tmpratur of nvironmnt, T (K) 98.5 Oprating prssur, p (atm) Partial prssur of H in th anod, p H, an (atm).6 Partial prssur of O in th cathod, p O, cat (atm).8 Partial prssur of N in th cathod, p N, cat (atm).59 Partial prssur of CO in th cathod, p CO, cat (atm).8 Partial prssur of H O in th cathod, p H O, cat (atm).5 Activation nrgy in th anod, E act, an (J mol - ) 53,5 Activation nrgy in th cathod, E act, cat (J mol - ) 77,3 Constant, m (m A - ).33 Constant, m By using Eqs. (), (6), (7), (), (3), th fficincy powr output of th hybrid systm can b, rspctivly, xprssd as

8 Int. J. Elctrochm. Sci., Vol. 6, 47 PM PH m( T / T ) M [ M ] H j T / T m[( M ) j m ( T / T )] (4) jah P PM PH nf. (5) It is sn from Eqs. (4) (5) that th prformanc of th MCFC-hat ngin hybrid systm dpnds on a st of thrmodynamic lctrochmical paramtrs such as th working tmpratur, currnt dnsity, synthsizd paramtrs m (i=, ), partial prssurs of lctrods gas compositions, i so on. Blow, numrical calculations ar carrid out basd on th data summarizd in Tabl, ths paramtrs ar kpt constant unlss mntiond spcifically. 3. GENERAL PERFORMANCE CHARACTERISTICS AND PARAMETRIC OPTIMUM CRITERIA Using Eqs. (6), (7), ()-(5), on can gnrat th curvs of th fficincy powr output of th MCFC, hat ngin hybrid systm varying with th currnt dnsity, as shown in Figs Figur 3. Th curvs of th fficincis of th hybrid systm, hat ngin, MCFC varying with th currnt dnsity, whr j is th currnt dnsity at th imum fficincy of th hybrid systm, M, m H, m ar th fficincis of th MCFC hat ngin in th hybrid systm at th imum, curvs I, II III corrspond to th cass of th hybrid systm, hat ngin, MCFC, rspctivly.

9 Int. J. Elctrochm. Sci., Vol. 6, 47 Figur 4. Th curvs of th powr dnsitis of th hybrid systm, hat ngin, MCFC varying with th currnt dnsity, whr j P is th currnt dnsitis at th imum powr dnsity P, P P ar th powr dnsitis of th hat ngin MCFC in th hybrid systm at th H,m imum M,m P, curvs I, II, III corrspond to th sam cass as thos in Fig. 3. Figur 5. Th powr dnsity vrsus fficincy curvs of th hybrid systm, hat ngin, MCFC, whr curv I, II, III corrspond to th sam cass as thos in Fig.3.

10 Int. J. Elctrochm. Sci., Vol. 6, 473 powr dnsity It is clarly sn from Figs. 3 4 that thr ar a imum fficincy a imum P for th hybrid systm th corrsponding currnt dnsitis ar j rspctivly. It is also sn from Figs. 3 4 that in th rgion of j j, both th fficincy th j P, powr output of th hybrid systm will dcras as th currnt dnsity j is dcrasd, whil in th rgion of j j, both th fficincy powr output of th hybrid systm will dcras as th P currnt dnsity j is incrasd. Obviously, th rgions of j j j P j ar not th optimally oprating rgion of th hybrid systm. Thus, th optimally oprating rgion of th currnt dnsity j for th MCFC-hat ngin hybrid systm should b dtrmind by j j j P. (6) To furthr undrst th prformanc charactristics of th hybrid systm, on can plot th powr dnsity vrsus fficincy curvs of th hybrid systm, as shown in Fig. 5. According to th optimum critrion of th currnt dnsity Fig. 5, on can furthr dtrmin th optimum rgions for th fficincy powr output as m (7) P m P, (8) P whr m Pm ar, rspctivly, th fficincy at th imum powr output th powr output at th imum fficincy. It is clarly sn from Figs. 3-5 that in th optimally oprating rgion, th fficincy powr output of th hybrid systm ar always largr than thos of th MCFC or hat ngin. It shows onc again that th application of th hybrid systm may ffctivly improv th prformanc of th MCFC systm. It should b pointd out that whn th hybrid systm is opratd in th optimum rgion, th powr output will incras as th fficincy is dcrasd, vic vrsa. Gnrally, th powr output P is vry small whn th hybrid systm achivs its imum fficincy th m fficincy m is not larg compard with whn th hybrid systm achivs its imum powr output P. Thus, th problm how to rasonably choos both th fficincy powr output in th optimal rgion of j j j P will bcom vry important in th practical optimum dsign opration of th hybrid systm. For this rason, w may introduc a multi-objctiv function which is dfind as th product of th fficincy with a wighting factor powr output [44-46], i.., Z P (9)

11 Int. J. Elctrochm. Sci., Vol. 6, 474 whr is th wighting factor which can b chosn according to th diffrnt rquirmnts for th fficincy powr output of th MCFC-hat ngin hybrid systm. Whn < λ <, th multi-objctiv function is rlatd to not only th fficincy powr output but also th concrt valu of th wighting factor. In such a cas, th multi-objctiv function is nithr th fficincy nor th powr output. Whn λ =, th multi-objctiv function bcoms on objctiv function, i.., th powr output. Whn, th multi-objctiv function tnds to zro, but it may b rwrittn as / λ / λ Z = ηp, which is th othr objctiv function, i.., th fficincy. Whn on pays qual attntion λ to both th fficincy powr output, on can choos. Blow, w will tak as an xampl to discuss th choic problm of th optimal currnt dnsity. Figur 6. Th curvs of th fficincy, powr dnsity multi-objctiv function of th hybrid systm varying with th currnt dnsity, whr j, jp jz ar th currnt dnsitis at th imum fficincy, powr dnsity multi-objctiv function, rspctivly. According to Eqs. (4), (5), (9), w can gnrat th curv of Z ~ j, as shown in Fig. 6, whr Z Z / A j Z is th currnt dnsity corrsponding to Z,. It is sn from Fig. 6 that Z first incrass thn dcrass with th incras of th currnt dnsity. This mans that thr always xists a imum for Z. Fig. 6 clarly shows that j j j. Thus, th optimal opration rgion j j j P η Z can b subdividd according to th diffrnt rquirmnts for both th fficincy th powr output. If mor attntion is mphasizd on th fficincy than on th powr output, th optimal opration rgion of th currnt dnsity should b P j j j Z. ()

12 Int. J. Elctrochm. Sci., Vol. 6, 475 If mor attntion is paid on th powr output than on th fficincy, th optimal opration rgion of currnt dnsity should b j j Z j P. () 4. DISCUSSION 4. Effcts of th oprating tmpratur T a b Figur 7. Th ffct of th oprating tmpratur on (a) th prformanc of th hybrid systm (b) th multi-objctiv function.

13 Int. J. Elctrochm. Sci., Vol. 6, 476 Th oprating tmpratur of th systm is an important factor bcaus it dirctly affcts th rvrsibl potntial as wll as th anod, cathod, ohm ovrpotntials of th ful cll. Fig. 7 clarly shows th ffcts of th oprating tmpratur on th prformanc of th hybrid systm th multiobjctiv function. It can b sn from th Fig. 7 (a) that th imum powr output its corrsponding fficincy as wll as th imum fficincy its corrsponding powr output incras as th oprating tmpratur is incrasd. Fig. 7 (b) shows that th imum multi-objctiv function its corrsponding currnt dnsity incrasd as th oprating tmpratur is incrasd. At highr oprating tmpraturs, th lctrods of MCFC ar mor ractiv th mass transfr within th ful cll is improvd, which rsult in a nt dcras in th ovrpotntials a nt incras in th rvrsibl potntial. Furthrmor, th prformanc of th hat ngin is naturally nhancd as th oprating tmpratur T is incrasd. Thus, th highr th oprating tmpratur of th MCFC-hat ngin hybrid systm is, th largr th fficincy, powr output, multi-objctiv function. 4. Effcts of m m () Whn m, i.., K, th influnc of th finit-rat hat transfr irrvrsibility btwn th hat ngin th hat rsrvoirs is ngligibl. In such a cas, Eqs. (), (4) (5) may b, rspctivly, simplifid as H T T C, () M m ( T / T ) C j, (3) M P jah n F M M m ( T / T j ) C, (4) whr C is th Carnot fficincy. Th powr output vrsus fficincy curv of th hybrid systm is shown by curv I in Fig. 8. Whn m >, th fficincy powr output of th hybrid systm ar of monotonically dcrasing functions of m. () Whn m =, th hat lak from th MCFC to th nvironmnt th irrvrsibl losss in th rgnrator ar ngligibl. In such a cas, Eqs. (), (4), (5) may b, rspctivly, simplifid as H, (5) T / T jm ( ) M

14 Int. J. Elctrochm. Sci., Vol. 6, 477 M ( M)[ ], (6) T / T jm ( ) M jah P M ( M)[ ]. (7) nf T / T jm( M) Th powr output vrsus fficincy curv of th hybrid systm is shown by curv II in Fig. 8. Whn m >, th fficincy powr output of th hybrid systm ar of monotonically dcrasing functions of m. Figur 8. Th powr dnsity vrsus fficincy curvs of th hybrid systm undr diffrnt conditions, whr m Pm ar th fficincy at th imum powr output P th powr output at th imum fficincy, rspctivly. Curvs I, II, III corrspond to th thr spcial cass: m = m = 4, m =. 45 m =, m = m =, rspctivly. (3) Whn m m =, th finit-rat hat transfr irrvrsibility btwn th hat ngin th hat rsrvoirs, th hat lak from th MCFC to th nvironmnt, th hat loss in th rgnrator ar ngligibl. In such a cas, Eqs. (3) (4) or Eqs. (6) (7) can b furthr simplifid as

15 Int. J. Elctrochm. Sci., Vol. 6, 478 ( ) (8) M M C jah P M ( M ) C nf, (9) rspctivly. Th powr output vrsus fficincy curv of th hybrid systm is shown by curv III in Fig. 8. In a practical MCFC-hat ngin hybrid systm, m > m >. Th gnral charactristics of th hybrid systm ar shown in Figs CONCLUSIONS With th hlp of th modl of an MCFC-hat ngin hybrid systm including multiirrvrsibilitis such as ovrpotntials in th lctrochmical raction, hat lak from th MCFC to th nvironmnt, non-prfct rgnration in th rgnrator, finit-rat hat transfr in th hat ngin, xprssions for th fficincy powr output of th hybrid systm ar analytically drivd, from which th gnral charactristics of th hybrid systm ar rvald th optimum critria of som important paramtrs ar dtrmind. Morovr, a multi-objctiv function is put forward to furthr subdivid th optimally oprating rgions according to th diffrnt rquirmnts for th fficincy powr output. Th influnc of th irrvrsibilitis on th prformanc of th hybrid systm is discussd in dtail. Th rsults obtaind hr may provid som thortical basis for th optimal dsign opration of practical MCFC-hat ngin hybrid systms. ACKNOWLEDGEMENTS This work has bn supportd by th National Natural Scinc Foundation (No ) th Fundamntal Rsarch Fund for th Cntral Univrsitis (No. G6), Popl s Rpublic of China. Rfrncs. D. C. Huang, P. J. Yu, F. J. Liu, S. L. Huang, K. L. Hsuh, Y. C. Chn, C. H. Wu, W. C. Chang, F. H. Tsau, Int. J. Elctrochm. Sci., 6 () 55.. M. EL Sayd Youssf, K. E. AL-NAdi, M. H. Khalil, Int. J. Elctrochm. Sci., 5 () Y. Kiros, Int. J. Elctrochm. Sci., (7) G. J. K. Acrs, J. Powr Sourcs, () A.Qi, B. Ppply, K. Karan, Ful Procss. Tchnol., 88 (7) G. Cacciola, V. Antonucci, S. Frni, J. Powr Sourcs, () R. O Hayr, S. W. Cha, W. Collla, F. B. Prinz, Ful Cll Fundamntals. John Wily & Sons. Inc., Nw York (6). 8. P. Tomczyk, J. Powr Sourcs, 6 (6) A.Dicks, A. Siddl, J. Powr Sourcs, 86 () 36.. P. S. Pak, Y. D. L, K. Y. Ahn, Enrgy, 34 (9) 93.

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